Multiple substitution effects in configuration interaction calculations

The common way of approximating multiple substitution effects by the unlinked cluster contribution based on the linked cluster theorem is investigated. Formally the analysis is done in a configuration interaction language without reference to diagrams. Using the linked cluster theorem a series expansion is then developed for the correction of a CI calculation, including double replacements only, for the erratic treatment of unlinked clusters. The first term in this series is closely related to what is generally referred to as Davidson's correction. The next term is proportional to the square of the correlation energy and is also very easy to calculate. Finally numerical examples are given illustrating the accuracy of the different approximations.